Merging vertical with slightly larger horizontal cylinder properly without creating Ngons?
Yes. Use the knife tool k to add these loops, while dissolving the one you already had and the triangle.



Remember to use c for 45 degree cuts and z to cut through to both sides.

Ideally when using cylinders I work with no more than 16 verts or it gets very messy and hard to keep the shape if you need loops to run parallel.